Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations (Q2805870)
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scientific article; zbMATH DE number 6580335
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations |
scientific article; zbMATH DE number 6580335 |
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13 May 2016
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fuzzy-valued functions
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fuzzy numbers
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fuzzy Volterra integral equations
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existence
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uniqueness
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Schauder's fixed point theorem
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Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations (English)
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The paper deals with continuous solutions of nonlinear fuzzy Volterra integral equations. It generalizes to the fuzzy case an existence theorem for nonlinear Volterra integral equations by \textit{A. Karoui} and \textit{A. Jawahdou} [Appl. Math. Comput. 216, No. 7, 2077--2091 (2010; Zbl 1196.45008)]. The existence proof is based on Schauder's fixed point theorem. Under additional conditions of Hölder's type, the uniqueness of solutions is also proved. The Lebesque integral is replaced by the Henstock integral for multivalued functions (cf. [\textit{C. Wu} and \textit{Z. Gong}, Fuzzy Sets Syst. 120, No. 3, 523--532 (2001; Zbl 0984.28010)]).
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